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In this article, we have considered the pattern formation during T-cell adhesion in a theoretical model. We propose a novel mechanism for the formation of intermediate patterns, which is based on the nucleation of TCR/MHCp microdomains throughout the contact zone and the diffusion of free receptors and ligands into the contact zone. This nucleation-diffusion mechanism is a self-assembly mechanism in the sense that it does not require active, ATP-driven processes. The mechanism leads to the intermediate inverted synapse pattern of T cells if the TCR/MHCp concentration is large enough. For smaller TCR/MHCp concentrations, the mechanism leads to multifocal intermediates which resemble patterns observed during thymozyte adhesion.

Other theory groups (Qi et al., 2001; S.-J. Lee et al., 2003; Raychaudhuri et al., 2003; Coombs et al., 2004) propose that the final T-cell pattern can be obtained by self-assembly. In the model of Qi et al. (2001), the central TCR/MHCp domain apparently results from the circular symmetry of the considered patterns. This symmetry prevents patterns with a single TCR/MHCp domain at the contact zone rim. Coombs et al. (2004) investigate equilibrium aspects of T-cell adhesion and focus on circularly symmetric patterns similar to Qi et al. (2001). In the models of S.-J. Lee et al. (2003) and Raychaudhuri et al. (2003), the central TCR/MHCp domain seems to arise from the boundary condition that the membrane separation at the contact zone rim is close to the LFA-1/ICAM-1 length of 40 nm. This boundary condition favors LFA-1/ICAM-1 domains at the rim, and repels TCR/MHCp domains from the contact zone rim. However, directly adjacent to the contact zone of two cells, the membrane separation quickly attains values much larger than the lengths of the receptor/ligand complexes. Therefore, we choose a more realistic boundary condition with a membrane separation at the rim which is significantly larger than the lengths of LFA-1/ICAM-1 and TCR/MHCp complexes.

For small TCR/MHCp concentrations, we obtain characteristic intermediate patterns with several distinct TCR/MHCp domains formed in self-assembly. These patterns resemble the multifocal synapse of thymozytes with several nearly circular and mobile TCR/MHCp domains. However, our patterns are only stable on the timescale of minutes. After a few minutes, domain coalescence leads to a single TCR/MHCp domain in our model. In contrast, the multifocal synapse of thymozytes is stable for hours. One reason for the pattern stability might be the thymozyte cytoskeleton. Unlike the cytoskeleton of mature T cells, the cytoskeleton of thymozytes presumably remains in a mobile, nonpolarized state which still allows cell migration (Hailman et al., 2002). The few TCR/MHCp clusters of thymozytes may be coupled to the cytoskeleton, thus following its movements.

A central question in immunology concerns the relation between the T-cell pattern formation on the one hand, and T-cell signaling and activation on the other hand (K.-H. Lee et al., 2002, 2003). We have focused here on the T-cell pattern formation. However, our model presupposes two early signaling events:A stop signal for any active T-cell migration on the APC surface. Active migration would result in contact zone movement during the pattern formation.

Lipid rafts have been suggested to play a central role in T-cell signaling (Janes et al., 1999; Viola and Lanzavecchia, 1999; Janes et al., 2000; Burack et al., 2002). Rafts are defined as nanoscale, ordered membrane domains rich in sphingolipids and cholesterol (Simons and Ikonen, 1997; Brown and London, 1998; Sharma et al., 2004). Lipid rafts are assumed to include or exclude membrane proteins, thus providing a microenvironment for membrane-anchored signaling molecules. In the T-cell membrane, the TCRs are seen to have an affinity for rafts (Janes et al., 2000; Simons and Toomre, 2000). Extracting cholesterol, one of the key components of rafts, from T-cell membranes has been shown to block the formation of the immunological synapse (Burack et al., 2002). However, extracting cholesterol after the synapse has been formed does not change the shape or area of the synapse domains (Burack et al., 2002). These experimental observations seem to indicate 1), that lipid rafts are involved in early signaling events required for the synapse formation, and 2), that the lipid phase separation leading to rafts is not the phase separation mechanism behind the T-cell pattern formation. As we have mentioned above in the Introduction, there is broad agreement that the lateral phase separation in the synapse is caused by the length mismatch between TCR/MHCp and ICAM-1/LFA-1 complexes. In principle, lipid raft formation may increase the tendency for lateral phase separation in the T-cell synapse, since rafts are assumed to be enriched in the central domain of the mature synapse (Burack et al., 2002). Currently, there is no experimental evidence for such an increase.

Lipid rafts may affect the lateral diffusion of receptors and ligands with strong raft affinity (Pralle et al., 2000). Rafts have been characterized as transient confinement zones (Dietrich et al., 2002) and seem to move as entities (Pralle et al., 2000). The lateral diffusion of membrane proteins may also be impaired by steric barriers from cytoskeleton fences (Kusumi and Sako, 1996) or by binding to the cytoskeleton (Dustin and Cooper, 2000). For simplicity, we have modeled the lateral diffusion of receptors, ligands, and glycoproteins as a hopping process with identical frequencies, which implies that these molecules have identical diffusion constants in the model. To relate the Monte Carlo time step of the hopping process to physical timescales, we took the typical diffusion constant D ≃ 1 μm2/s (Almeida and Vaz, 1995) as an estimate. A single Monte Carlo step then corresponds to 1 ms (see Adhesion Dynamics in the Absence of Cytoskeletal Transport Processes, above), which leads to the pattern evolution times shown in Figs. 3, ​,4,4, and ​and7.7. A twofold smaller diffusion constant would lead to a twofold increase in these evolution time estimates. It is important to note that the relaxation dynamics of the membrane separation field is significantly faster than the diffusion dynamics (see Adhesion Dynamics in the Absence of Cytoskeletal Transport Processes, above). In other words, the membrane separation quickly adapts to a given distribution of the macromolecules. Therefore, parameters like the bending rigidity κ and the lateral tension γ, which govern the relaxation dynamics, do not directly affect the pattern evolution timescales.

T cells and APCs have been observed to form numerous dynamic, short-lived contacts with a duration of a few minutes in a three-dimensional collagen model of the extracellular matrix (Gunzer et al., 2000). Based on these observations, a serial-encounter model of T-cell activation has been postulated (Friedl and Gunzer, 2001), which contrasts the view that T cells have to form a long-lasting, mature synapse for activation (Dustin et al., 2001b). Recent in vivo experiments show that T cells and APCs both have multiple short encounters with a duration of minutes and long-lasting stable contacts with a duration up to an hour and more, in different phases of T-cell activation (Mempel et al., 2004). We have focused here on the pattern formation during long-lasting contacts between T cells and APCs. However, our simulations show that relatively large TCR/MHCp domains already arise in the first seconds and minutes after adhesion. These domains may play an important role in signaling events during short cell encounters.

We have applied our model here to T-cell adhesion, using the specific lengths of the TCR/MHCp and ICAM-1/LFA-1 complexes in the interaction potentials (Eqs. 3 and 4). However, the model is rather general and also applies to other cell adhesion events. We have previously considered a simpler membrane system with stickers and repellers (Weikl et al., 2002). The phase separation into sticker- and repeller-rich domains is driven by the length difference between the two molecule types. In the cell adhesion geometry, we obtained intermediate patterns which are similar to those presented here. A difference to T-cell membranes is that the repeller-rich domains are unbound. Large-scale membrane fluctuations in these domains then drive the final sticker clusters toward the center of the contact zone, at least for the free boundary conditions with unconstrained membrane separation at the contact zone rim (Weikl et al., 2002). In contrast, the coexisting TCR/MHCp and ICAM-1/LFA-1 domain types of T cells are both bound, and large-scale membrane fluctuations are suppressed.

Natural killer (NK) cells form an inverted synapse, consisting of a peripheral ring of short HLA-C/KIR complexes and a central domain with the longer LFA-1/ICAM-1 complexes. The formation of the NK cell synapse seems not to depend on active cytoskeletal processes, since ATP depletion or disruption of the cytoskeleton has no effect on the pattern (Davis et al., 1999; Fassett et al., 2001). A possible explanation for the NK cell synapse is the metastability of the inverted pattern in the absence of active cytoskeletal processes. Without active transport, the inverted intermediate synapse persists up to an hour in our model.